Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows

Vitolo, Renato and Glendinning, Paul and Gallas, Jason A.C. (2011) Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows. [MIMS Preprint]

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Abstract

Infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows. Here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow. We show that spirals associated with periodicity hubs emerge/accumulate at the folding of certain fractal-like sheaves of Shilnikov homoclinic bifurcations of a common saddle-focus equilibrium. The specific organization of hub networks is found to depend strongly on the interaction between the homoclinic orbits and the global structure of the underlying attractor.

Item Type: MIMS Preprint
Additional Information: CICADA
Uncontrolled Keywords: homoclinic, hub
Subjects: PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems
Depositing User: Professor Paul Glendinning
Date Deposited: 04 Jul 2011
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1645

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